The radicals of a semigroup
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- by Rebecca Slover PDF
- Trans. Amer. Math. Soc. 204 (1975), 179-195 Request permission
Abstract:
This paper investigates various radicals and radical congruences of a semigroup. A strongly prime ideal is defined. It is shown that the nil radical of a semigroup is the intersection of all strongly prime ideals of the semigroup. Furthermore, a semigroup with zero element is nil if and only if it has no strongly prime ideals. We investigate the question of when the left and right radical congruence relations of various radicals are equal. Some theorems analogous to theorems concerning the radicals of rings are also proved.References
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Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 204 (1975), 179-195
- MSC: Primary 20M10
- DOI: https://doi.org/10.1090/S0002-9947-1975-0369584-6
- MathSciNet review: 0369584